Analytical asymptotic approximations for large amplitude nonlinear free vibration of a dielectric elastomer balloon

Dafeng Tang, C. W. Lim, Ling Hong, Jun Jiang, Siu Kai Lai

Research output: Journal article publicationJournal articleAcademic researchpeer-review

23 Citations (Scopus)


Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period and periodic solution for a spherical dielectric elastomer balloon subjected to static pressure and voltage are derived through an analytical method, called the Newton–harmonic balance (NHB) method. The elastomeric spherical balloon is modeled as an autonomous nonlinear differential equation with general and negatively powered nonlinearities. The NHB method enables to linearize the governing equation prior to applying the harmonic balance method. Even for such a nonlinear system with negatively powered variable and non-classical non-odd nonlinearity, the NHB method is capable of deriving highly accurate approximate solutions. Several practical examples with different initial stretch ratios are solved to illustrate the dynamic inflation of elastomeric spherical balloons. When the initial amplitude is sufficiently large, the system will lose its stability. Comparison with Runge–Kutta numerical integration solutions is also presented and excellent agreement has been observed.
Original languageEnglish
Pages (from-to)2255-2264
Number of pages10
JournalNonlinear Dynamics
Issue number3
Publication statusPublished - 1 May 2017


  • Analytical approximation
  • Dielectric elastomer
  • Newton–harmonic balance
  • Nonlinear free vibration

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this